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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/934| ITERATING THE CES`ARO OPERATORS | |
| FERNANDO GALAZ FONTES | |
| Acceso Abierto | |
| Atribución-NoComercial-CompartirIgual | |
| Operadores de Cesaro | |
| The discrete Ces`aro operator C associates to a given complex sequence s = {sn} the sequence Cs ≡ {bn}, where bn = s0+···+sn n+1 , n = 0, 1, . . .. When s is a convergent sequence we show that {Cns} converges under the sup-norm if, and only if, s0 = limn→∞ sn. For its adjoint operator C∗, we establish that {(C∗)ns} converges for any s ∈ 1. The continuous Ces`aro operator, Cf(x) ≡ 1 x x 0 f(s)ds, has two versions: the finite range case is defined for f ∈ L∞(0, 1) and the infinite range case for f ∈ L∞(0,∞). In the first situation, when f : [0, 1] → C is continuous we prove that {Cnf} converges under the sup-norm to the constant function f(0). In the second situation, when f : [0,∞) → C is a continuous function having a limit at infinity, we prove that {Cnf} converges under the sup-norm if, and only if, f(0) = limx→∞ f(x). | |
| American Mathematical Association | |
| 2008 | |
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| publishedVersion - Versión publicada | |
| Aparece en las colecciones: | Matemáticas |
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